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K-convexity In Rn
K-convexity in Rn is a mathematical concept. Formula Let ''\Kappa''= (''K0'',''K1'',...,''Kn'') to be a vector of (n+1) nonnegative constants and define a function \Kappa(.): \Re_+^n → \Re_+^1 as follows: \Kappa(x) = ''K0''\delta(''e''x) + \sum_^n''Ki''\delta(x_i), where ''e'' = (1,1,...,1) ∈ \Re^n, \Re_+^n = \, \delta(0) = 0 and \delta(z)= 1 for all z > 0. The concept of K-convexity generalizes ''K'' -convexity introduced by Scarf (1960) to higher dimensional spaces and is useful in multiproduct inventory problems with fixed setup costs. Scarf used ''K'' -convexity to prove the optimality of the (s, S) policy in the single product case. Several papers are devoted to obtaining optimal policies for multiple product problems with fixed ordering costs. This definition introduced by Gallego and Sethi (2005) is motivated by the joint replenishment problem when we incur a setup cost ''K0'', whenever we order an item or items and an individual setup cost ''Ki'' for each item i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-convex Function
''K''-convex functions, first introduced by Scarf, are a special weakening of the concept of convex function In mathematics, a real-valued function is called convex if the line segment between any two points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of poin ... which is crucial in the proof of the optimality of the (s,S) policy in inventory control theory. The policy is characterized by two numbers and , S \geq s, such that when the inventory level falls below level , an order is issued for a quantity that brings the inventory up to level , and nothing is ordered otherwise. Gallego and Sethi Gallego, G. and Sethi, S. P. (2005). ''K''-convexity in ℜn. ''Journal of Optimization Theory & Applications,'' 127(1):71-88. have generalized the concept of ''K''-convexity to higher dimensional Euclidean spaces. Definition Two equivalent definitions are as follows: Definition 1 (The orig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herbert Scarf
Herbert Eli "Herb" Scarf (July 25, 1930 – November 15, 2015) was an American mathematical economist and Sterling Professor of Economics at Yale University. Education and career Scarf was born in Philadelphia, the son of Jewish emigrants from Ukraine and Russia, Lene (Elkman) and Louis Scarf. During his undergraduate work he finished in the top 10 of the 1950 William Lowell Putnam Mathematical Competition, the major mathematics competition between universities across the United States and Canada. He received his PhD from Princeton in 1954, supervised by Salomon Bochner. Contributions Among his notable works is a seminal paper in cooperative game in which he showed sufficiency for a core (economics) in general balanced games. Sufficiency and necessity had been previously shown by Lloyd Shapley for games where players were allowed to transfer utility between themselves freely. Necessity is shown to be lost in the generalization. Recognition Scarf received the 1973 Frederi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Operations Research
''Mathematics of Operations Research'' is a quarterly peer-reviewed scientific journal established in February 1976. It focuses on areas of mathematics relevant to the field of operations research such as continuous optimization, discrete optimization, game theory, machine learning, simulation methodology, and stochastic models. The journal is published by INFORMS (Institute for Operations Research and the Management Sciences). the journal has a 2017 impact factor of 1.078. History The journal was established in 1976. The founding editor-in-chief was Arthur F. Veinott Jr. (Stanford University). He served until 1980, when the position was taken over by Stephen M. Robinson, who held the position until 1986. Erhan Cinlar served from 1987 to 1992, and was followed by Jan Karel Lenstra (1993-1998). Next was Gérard Cornuéjols (1999-2003) and Nimrod Megiddo (2004-2009). Finally came Uri Rothblum (2009-2012), Jim Dai (2012-2018), and the current editor-in-chief Katya Scheinberg ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Suresh P
Suresh is an Indian masculine given name originating in the Sanskrit word ' (compound of ' and '). Its meaning is "Ruler of Gods" and it has been used an epithet for the Hindu gods Indra, Brahma, Vishnu and Shiva. People named Suresh include: *Suresh (actor), Indian actor in Telugu and Tamil films *Suresh (director), Tamil film director *Suresh Balaje, Indian film producer * Suresh Bharadwaj, Indian politician *Suresh Gopi (born 1960), Indian Malayalam film actor *Suresh Heblikar, Indian Kannada film actor *Suresh Joachim, Tamil Canadian film actor, producer and multiple Guinness World Record holder *Suresh Joshi, Indian poet, writer and literary critic * Suresh Krishna, Indian Malayali film actor *Suresh Krissna, Indian Tamil film director *Suresh Kumar (government official), American economist and businessman, Director-General of the U.S. Foreign Commercial Service *Suresh Oberoi, Indian Hindi movie actor *Suresh Pachouri, Indian politician *Suresh Raina, Indian cricketer *Sures ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |